APBRmetrics

Mike G · Posted: Thu May 20, 2010 5:05 pm Post subject: **Replacement player value**

If .80 of average efficiency differential (ED) is Replacement Level (RL) play, then a team of RL players, averaging a score of 80-100, would be expected to win about 5% of their games. They might go 4-78.

A team that averages 70-100 should only win 1% of their games. That's pretty close to 0-82.

To win 10 of 82 games, RL would be around .86 or .87 ED.

No team has ever been as bad as 4-78, and no team has ever been without any good player for a whole season. Of course, a team might have some players worse than RL and still average RL.

Here are 2010 league average per-36 rates, and .80 of those rates:

BobboFitos · Joined: 21 Feb 2009 Posts: 201 Location: Cambridge, MA

Good stuff. The question though, focusing on scoring per 36, is are we assuming that .8 player is taking on the same offensive burden? Also, .8 TO of 2 per 36 should be 2.5 since it's the inverse of .8, no? If the shot attempts are the same, then their TS is falling from say an average value of ~54.3 to generate 15 per 36 (or 13.81 raw true shooting attempts) down to ~43.4 TS.*

*I basically figured to score 15 per 36 on the average NBA TS requires 13.81 TSA, so if you're scoring only 12 points on those same shot attempts, that's the relative drop in TS.

~~~

Do people view the worst historical record as a team full of replacement players? I don't. The 9 win 1973 76ers actually fell well below their pyth, but employed several players who had long-ish NBA careers. (Suggesting that they were not truly replaceable in the minimal sense) Granted I don't know anything about these players outside of skimming bref/looking at their career stats, but I think setting the door at a "10 win team" isn't really the hypothetical floor.

Does a team full of replacements - that is, a team that doesn't have ANYONE on the roster that would be deemed an improvement for any other team (maybe?) even win a game? There's a huge gap between a -20 and -30 PD.
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DSMok1 · Posted: Fri May 21, 2010 12:04 pm Post subject:

A good start to studying replacement level would be to study baseball's accepted methodology. Hardball times has a few articles, for starters.

Basketball skill over the whole world's population is approximately a bell curve. We can all agree on that, right?

The players in the NBA are basically the right tail of that curve--so the curve should look fairly exponential, in terms of player quality from left to right.

However, once you get down to below average, there is a strong selective sampling issue--not every player of that quality actually is playing in the NBA. We end up seeing a slightly left-skewed graph of the quality of players in the NBA. Something like a log-normal distribution of sigma 1/2. Once the players get bad enough, none of them are in the NBA.

From a team's perspective, they are trying to get enough quality players on the court at once to win games. Is an NBA average player worth something? Yes, by definition. NBA-average players would win 41 games. What about somebody a little worse than average? Yes, he would help out also. You may need to play him, and players of his caliber (say an APM of -2) are not freely available.

So what is the threshold of replacement level? There is the rub. It is not the best player who isn't starting. That's way too high. It's probably above the 15th player on the bench--he could be old and bad but still under contract, or a youngster expected to develop.

Here's Tom Tango's definition:

mtamada · Joined: 28 Jan 2005 Posts: 377

Mike G · Posted: Sat May 22, 2010 6:55 pm Post subject:

Are Win Shares (or WS/48) already above a replacement level?

This season, there were 368 players w >200 minutes and >0 WS/48. (Along with 18 who were negative.)
That's about 12.3 per team.

At 600 minutes, 310 positive and just 8 negative.
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DSMok1 · Posted: Sat May 22, 2010 9:16 pm Post subject:

Mike G · Posted: Sun May 23, 2010 6:14 am Post subject:

But if by definition only players above replacement level are adding wins, then only negative WS/48 players would be considered sub-replacement level.

If so, then .000 WS/48 = RL

Whether 12 per team is the 'right' number of >RL players, or whether the remaining 3 players x 30 rosters ('project' players, practice guys, etc) effectively ensures that there are no better players available, this might be close.

It's still possible for replacements to generate wins, as their distribution of performance varies from game to game. A whole team of RP's (and sub-RP's) can get it together against a merely bad team on a bad night, and pull off a win or 2, out of 82.

In the real world, though, the RP team is in a vacuum against relentless pressure. A Stackhouse or a Rodman will surely come out of exile or retirement and suit up.

Found this thread which discusses replacement level:
viewtopic.php?t=2153
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DSMok1 · Posted: Sun May 23, 2010 8:24 am Post subject:

gabefarkas · Joined: 31 Dec 2004 Posts: 1313 Location: Durham, NC

Instead of trying to theoretically come up with how many wins produced a replacement player would provide, why not try to come up with it empirically? What I mean is to try to identify actual replacement players, and then look at what they actually did on the court.

If we wanted to, from there we could even do permutation distributions, bootstrapping, jackknife, or any other resampling technique to come up with an empirical distribution for what would be expected from a replacement player.

So, what if we came up with a list of who we believe are actual replacement players? A starting point might be something along the lines of:
Aaron Gray
Aaron Miles
Alex Acker
Allan Ray
Andre Emmett
Awvee Storey
Bernard Robinson
Britton Johnsen
Casey Jacobsen
Chase Budinger
Chris Jefferies
Chris Quinn
Chris Taft
Daniel Ewing
Deng Gai
Dijon Thompson
Frank Williams
Gabe Pruitt
Josh McRoberts
etc etc etc

Does that make sense? Come up with a list of what you would consider replacement players, and then derive an empirical distribution from there.

Carlos · Joined: 21 Jan 2005 Posts: 64 Location: Montevideo, Uruguay

What about looking at guys picked from the NBDL and undrafted players or midseason additions? It's relatively rare, but each year you see a few guys enter the league who were truly obtained at minimum costs. I remember the Grizziles a few years ago had all of their PGs injured and picked Elliot Perry basically off the street to play for a couple of games. It was unusual, sure, but I'd bet that every year there are a few cases like that, of teams playing truly marginal guys because of health issues.

Mike G · Posted: Sun May 23, 2010 12:46 pm Post subject:

DLew · Joined: 13 Nov 2006 Posts: 224

Mike,

You always seem hung up by anything that suggests teams are not optimizing. Why is this? It seems clear that many teams are not. Some teams play guys who are worse than the freely available players. Do you disagree?

schtevie · Joined: 18 Apr 2005 Posts: 413

Can someone say, slowly and clearly, why one should be impressed with the concept of a replacement level player? In particular, why is it useful at all in discussing basketball?

I kind of can see in baseball, where the production function of the game is relatively simple, defining some inherently arbitrary below-average standard as a benchmark for comparing player values and this becoming a convention over time. But basketball is different. The production function is very complicated; it is not clear what the below-average standard should be; and it is difficult to measure player contributions precisely.

It is far more intuitive to at least eliminate one of these problems and have the benchmark of comparison be the average player, whether this value be zero (in terms of net points) or 8.2 (for per game WS).

The futility can be illustrated with 2007-08 data, chosen to utilize Ilardi & Barizlai's multi-year APM numbers as estimates of value. Let's take as an arbitrary starting point, the 360th ranked player in minutes per game (so, kind of the 12th man on the 30th team): Malik Rose, playing 10.1 minutes per game. Finding the 15 players above and below this mark (again, arbitrary) that meet the minimum minutes cut-off for I & B's estimates, the average multi-year APM is -3.0.

Might this replacement level definition be consistent over time? Perhaps. Ten minutes seems plausible. But even if the contribution of ten minute players hurt their teams to the tune of 3 points per 100 possessions on average, there is a great deal of dispersion around the mean. The standard deviation in the instance is 4.1, the estimates ranging from Ronnie Price's 7.17 to Dominic McGuire's -12.07. As such, what is the point of the exercise? What does the concept of a replacement level player gain us?

Kevin Pelton · Posted: Sun May 23, 2010 3:07 pm Post subject:

http://web.archive.org/web/20040404040837/http://www.hoopsworld.com/article_7557.shtml

DSMok1 · Posted: Sun May 23, 2010 4:56 pm Post subject: